What you're describing is true, but also different from what the original comment is talking about. There is a global trend to urbanization, yes. The original comment isn't talking about moving from rural to urban; what they say applies to moving from one city to another.
Moreover, at an individual scale, moving for better opportunities doesn't mean one has to leave family and friends. For example, my grandma: she was very poor, and moved a few times different cities looking for a better life. This meant moving with her whole family, and/or moving where other family was. After she married my grandpa, he got job opportunities in both Guadalajara and Mexico City. I'm sure they could've done better in Mexico City, since it's the capital, but they chose Guadalajara due to proximity to family. Her mom eventually moved to Guadalajara too.
Another, more recent example from my family: my uncle. He had the opportunity to move for a very good job, but didn't take it since it was far from family. My brother moved cities for college, but specifically to one where he would be close to family.
One thing is moving wherever it takes for the sake of going to a specific school, working at a specific job, living in a specific dream home or dream city. That is very American. Another one is still looking for opportunities, but framing everything in terms of your family and friends; ie, what's the best job, school, home I can find close to my family? That's much more Latin American and much less common, in my experience, in the USA.